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Über dieses Buch

Mechanical engineering, an engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solu­ tions, among others. The Mechanical Engineering Series is a new series, featuring graduate texts and research monographs, intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate edu­ cation and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the first page of the volume. The areas of concentration are applied mechanics, biomechanics, computa­ tional mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Professor Marshek, the consulting editor for dynamic systems and con­ trol, and I are pleased to present this volume of the series: Underconstrained Structural Systems by Professor Kuznetsov. The selection of this volume underscores again the interest of the Mechanical Engineering Series to pro­ vide our readers with topical monographs as well as graduate texts.

Inhaltsverzeichnis

Frontmatter

Fundamentals

Frontmatter

1. Statical-Kinematic Analysis

Abstract
The objective of this chapter is to modernize and further develop the basic concepts of statical-kinematic analysis, and to refine the classification of generic structural systems. This is done with a view to both a rigorous treatment of the topic and the development of analytical criteria amenable to computerized analysis.
E. N. Kuznetsov

2. Systems with Infinitesimal Mobility

Abstract
For a structural engineer, infinitesimal mobility has traditionally been an obscure side issue. In a typical text on structural analysis, systems with infinitesimal mobility are discussed very briefly, labeled geometrically unstable, hence unsuitable for practical applications, and abandoned from further consideration. For a mechanical engineer, infinitesimal mechanisms have been even less interesting, as they lack the quintessential feature of mobility. One of very few applications of such systems has been their use as a “force amplifier”.
E. N. Kuznetsov

3. Systems Involving Unilateral Constraints

Abstract
A unilateral constraint is an idealized model of a structural component that limits some linear or angular distance to values either no greater than, or no less than, a certain magnitude. Unlike bilateral constraints, unilateral constraints are binding in only one sense of direction. Some structural components modeled as unilateral constraints in tension are wires, cables, flexible bands, membranes, fabrics, and rectilinear pin-bar chains. Situations giving rise to unilateral constraints in compression include contact problems, stacks of building blocks, springs with collapsed coils, components made of brittle, low-tensile strength materials with no reinforcement, and all kinds of liquid and granular media. Typical examples of angular, or bending, unilateral constraints are a door hinge, a spherical hinge with restraints, and a concrete beam with only a bottom reinforcement. The three most common types of unilateral constraints are shown schematically in Fig. 1.
E. N. Kuznetsov

4. Kinematic and Elastic Mobility

Abstract
Mobility, either virtual or kinematic, is a definitive feature of underconstrained structural systems. The two types of mobility are intricately intertwined. For instance, when a quasi-variant system (type III) made of a real, flexible material is subjected to a perturbation load, it undergoes displacements and constraint variations bringing it out of its singular configuration. As a result, the system acquires kinematic mobility, i.e., the possibility of finite displacements without any additional constraint variations. Under the same conditions, a quasi-invariant system (type II) behaves differently: in a new configuration it loses even its virtual mobility and becomes capable of supporting an arbitrary load.
E. N. Kuznetsov

Applications to Particular Systems

Frontmatter

5. Cables and Cable Systems

Abstract
A cable is the simplest continuous underconstrained structural system. Its analytical model is a flexible wire, or a fiber, i.e., a perfectly flexible structural element capable of resisting only one type of force, axial tension. A cable is a variant system, with the exception of a rectilinear configuration with both ends fixed, when it is quasi-variant. The role of the cable as a structural component in engineering applications is diverse and growing. One of the reasons is the very logic of technical progress, resulting in an ever-increasing materials strength. As a matter of principle, tension is the only type of stress fully capitalizing on this trend. The cable also serves as an analytical model for a membrane in a uniaxial stress state. This can be either a wrinkling membrane or a membrane in a state of plane strain, like a membrane trough under a hydrostatic load considered in Section 1.
E. N. Kuznetsov

6. Nets

Abstract
A net is an assembly of two noncoinciding arrays of linear elements (cables, wires, or fibers) located on one surface. Each element usually intersects only the elements of the other array, although singular points, like the pole in a radial-hoop system, may exist. Unless the intersections are fastened, mutual in-surface slipping (but not delamination) of the cables is assumed possible. Accordingly, the described model applies not only to cable or fiber nets proper, but also to two-ply fabrics with a conventional weave. In this case, the possibility or absence of fiber slipping are attributable, respectively, to negligible or very high friction. Regardless of whether or not the element intersections are fastened, a net is an underconstrained structural system. It allows singular configurations, of which some lack kinematic mobility (quasi-variant nets).
E. N. Kuznetsov

7. Axisymmetric Nets

Abstract
The general results of the preceding chapter are elaborated on and applied here to axisymmetric nets. This class of nets is segregated for two main reasons. First, axisymmetric nets are widely used in engineering applications, including situations where a suitable segment of an axisymmetric net approximates a general-type surface with an acceptable precision. Second, their analysis reduces to ordinary differential equations, admitting in many cases closed-form first integrals and making unnecessary the use of tensors. The simpler analysis facilitates better understanding and provides additional insights into the structural behavior of all nets, not just axisymmetric ones.
E. N. Kuznetsov

8. Membranes

Abstract
In structural mechanics, a membrane is modeled analytically as a material surface devoid of bending stiffness and resisting only tangential (in-surface) membrane forces—normal and shearing. The absence of bending stiffness, strictly speaking, implies no resistance to compression stress as well. However, a momentless shell supporting compression is a common model in structural analysis. It is sometimes referred to as a membrane shell, especially when it is necessary to distinguish it from a true, or ideal, membrane, which is a system with unilateral constraints in tension.
E. N. Kuznetsov

9. Other Underconstrained Systems and Contact Problems

Abstract
This chapter comprises a selection of underconstrained structural systems of which some are new and others are combinations of the already familiar components such as cables, nets, and membranes. The subject of the first section is a band or a cable-band assembly. These assemblies involve one or more arrays of structural members in the form of thin narrow flexible bands, which represent a relatively new addition to the list of generic structural components. When used in place of one (or, possibly, both) of the cable arrays of a net, bands advantageously combine load-carrying and surface-cladding functions. The kinematic properties of a band, together with the arrangement of band or cable-band intersections, account for some interesting features in the system statics and kinematics. At the same time, the properties of a band as a structural component impose certain restrictions on the feasible geometry of a band or cable-band system as compared with a similar cable net.
E. N. Kuznetsov

10. Related Applications

Abstract
Several different applications presented in this chapter deal with some aspects of structural behavior typical of underconstrained systems. The first section is concerned with systems that exhibit the type of behavior called kinematic adaptivity: the system kinematically adapts to an applied load by acquiring a configuration that is, in a sense, most suitable for supporting the load. This feature is very useful in actively controlled systems, in particular, those implementing the concept of statically controlled geometry.
E. N. Kuznetsov

Backmatter

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